cp's OEIS Frontend

A344091 Flattened tetrangle of all finite multisets of positive integers sorted first by sum, then by length, then colexicographically.

%I A344091 #14 Sep 22 2023 09:04:42
%S A344091 1,2,1,1,3,1,2,1,1,1,4,2,2,1,3,1,1,2,1,1,1,1,5,2,3,1,4,1,2,2,1,1,3,1,
%T A344091 1,1,2,1,1,1,1,1,6,3,3,2,4,1,5,2,2,2,1,2,3,1,1,4,1,1,2,2,1,1,1,3,1,1,
%U A344091 1,1,2,1,1,1,1,1,1
%N A344091 Flattened tetrangle of all finite multisets of positive integers sorted first by sum, then by length, then colexicographically.
%C A344091 First differs from A334302 for partitions of 9.
%C A344091 The zeroth row contains only the empty partition.
%C A344091 A tetrangle is a sequence of finite triangles.
%H A344091 Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order">Lexicographic and colexicographic order</a>
%e A344091 Tetrangle begins:
%e A344091   0: ()
%e A344091   1: (1)
%e A344091   2: (2)(11)
%e A344091   3: (3)(12)(111)
%e A344091   4: (4)(22)(13)(112)(1111)
%e A344091   5: (5)(23)(14)(122)(113)(1112)(11111)
%e A344091   6: (6)(33)(24)(15)(222)(123)(114)(1122)(1113)(11112)(111111)
%t A344091 Table[Reverse/@Sort[IntegerPartitions[n]],{n,0,9}]
%Y A344091 The version for lex instead of colex is A036036.
%Y A344091 Starting with reversed partitions gives A036037.
%Y A344091 Ignoring length gives A211992 (reversed: A080576).
%Y A344091 Same as A334301 with partitions reversed.
%Y A344091 The version for revlex instead of colex is A334302.
%Y A344091 The Heinz numbers of these partitions are A334433.
%Y A344091 The strict case is A344089.
%Y A344091 A026791 reads off lexicographically ordered reversed partitions.
%Y A344091 A080577 reads off reverse-lexicographically ordered partitions.
%Y A344091 A112798 reads off reversed partitions by Heinz number.
%Y A344091 A193073 reads off lexicographically ordered partitions.
%Y A344091 A296150 reads off partitions by Heinz number.
%Y A344091 Cf. A000041, A026793, A124734, A185974, A228531, A246688, A296774, A334433, A334435, A334438, A334439, A334441, A334442, A344086, A344090.
%K A344091 nonn,tabf
%O A344091 0,2
%A A344091 _Gus Wiseman_, May 12 2021